Editing Hubble's law (section)

== Discovery ==
[[File:Three steps to the Hubble constant.jpg|thumb|upright=2.2|Three steps to the Hubble constant<ref>{{cite web|title=Three steps to the Hubble constant|url=https://www.spacetelescope.org/images/opo1812a/|website=www.spacetelescope.org|access-date=26 February 2018}}</ref>]]

A decade before Hubble made his observations, a number of [[physicists]] and [[mathematician]]s had established a consistent theory of an expanding universe by using [[Einstein field equations]] of [[general relativity]]. Applying the most [[Cosmological principle|general principles]] to the nature of the [[universe]] yielded a [[Dynamics (mechanics)|dynamic]] solution that conflicted with the then-prevalent notion of a [[static universe]].

=== Slipher's observations ===
In 1912, [[Vesto M. Slipher]] measured the first [[Doppler shift]] of a "[[spiral nebula]]" (the obsolete term for spiral galaxies) and soon discovered that almost all such objects were receding from Earth. He did not grasp the cosmological implications of this fact, and indeed at the time it was [[Shapley–Curtis debate|highly controversial]] whether or not these nebulae were "island universes" outside the Milky Way galaxy.<ref>{{cite journal |last=Slipher |first=V. M. |date=1913 |title=The Radial Velocity of the Andromeda Nebula |journal=[[Lowell Observatory Bulletin]] |volume=1 |issue=8 |pages=56–57 |bibcode=1913LowOB...2...56S }}</ref><ref>{{Cite journal |last=Slipher |first=V. M. |date=1915 |title=Spectrographic Observations of Nebulae |journal=[[Popular Astronomy (US magazine)|Popular Astronomy]] |volume=23 |pages=21–24 |bibcode=1915PA.....23...21S }}</ref>

=== FLRW equations ===
{{Main|Friedmann–Lemaître–Robertson–Walker metric}}
In 1922, [[Alexander Friedmann]] derived his Friedmann equations from [[Einstein field equations]], showing that the universe might expand at a rate calculable by the equations.<ref>{{Cite journal |last=Friedman |first=A. |date=1922 |title=Über die Krümmung des Raumes |journal=[[Zeitschrift für Physik]] |language=de |volume=10 |issue=1 |pages=377–386 |bibcode=1922ZPhy...10..377F |doi=10.1007/BF01332580 |s2cid=125190902}} Translated to English in {{Cite journal |last1=Friedmann |first1=A. |date=1999 |title=On the Curvature of Space |journal=[[General Relativity and Gravitation]] |volume=31 |issue=12 |pages=1991–2000 |bibcode=1999GReGr..31.1991F |doi=10.1023/A:1026751225741 |s2cid=122950995}}</ref> The parameter used by Friedmann is known today as the [[Scale factor (cosmology)|scale factor]] and can be considered as a [[Scale invariance|scale invariant]] form of the [[Proportionality (mathematics)|proportionality constant]] of Hubble's law. Georges Lemaître independently found a similar solution in his 1927 paper discussed in the following section. The Friedmann equations are derived by inserting the [[Friedmann–Lemaître–Robertson–Walker metric|metric for a homogeneous and isotropic universe]] into Einstein's field equations for a fluid with a given [[density]] and [[pressure]]. This idea of an expanding spacetime would eventually lead to the [[Big Bang]] and [[Steady State Theory|Steady State]] theories of [[cosmology]].

=== Lemaître's equation ===
In 1927, two years before Hubble published his own article, the Belgian priest and astronomer Georges Lemaître was the first to publish research deriving what is now known as Hubble's law. According to the Canadian astronomer [[Sidney van den Bergh]], "the 1927 discovery of the expansion of the universe by Lemaître was published in French in a low-impact journal. In the 1931 high-impact English translation of this article, a critical equation was changed by omitting reference to what is now known as the Hubble constant."<ref>{{cite journal|last1=van den Bergh|first1=Sydney|title=The Curious Case of Lemaître's Equation No. 24|journal=Journal of the Royal Astronomical Society of Canada|volume=105|issue=4|page=151|arxiv=1106.1195|year=2011|bibcode=2011JRASC.105..151V}}</ref> It is now known that the alterations in the translated paper were carried out by Lemaître himself.<ref name = Livio /><ref>{{cite book|last1=Block|first1=David|title='Georges Lemaitre and Stigler's law of eponymy' in Georges Lemaître: Life, Science and Legacy|date=2012|publisher=Springer|pages=89–96|edition=Holder and Mitton}}</ref>

=== Shape of the universe ===
Before the advent of modern cosmology, there was considerable talk about the size and [[shape of the universe]]. In 1920, the [[Great Debate (astronomy)|Shapley–Curtis debate]] took place between [[Harlow Shapley]] and [[Heber Doust Curtis|Heber D. Curtis]] over this issue. Shapley argued for a small universe the size of the Milky Way galaxy, and Curtis argued that the universe was much larger. The issue was resolved in the coming decade with Hubble's improved observations.

=== Cepheid variable stars outside the Milky Way ===
Edwin Hubble did most of his professional astronomical observing work at [[Mount Wilson Observatory]],<ref>{{cite journal | last = Sandage | first = Allan | title = Edwin Hubble 1889–1953 | date = December 1989 | journal = Journal of the Royal Astronomical Society of Canada | volume = 83 | issue = 6 | pages = 351–362| bibcode = 1989JRASC..83..351S }}</ref> home to the world's most powerful telescope at the time. His observations of [[Cepheid variable]] stars in "spiral nebulae" enabled him to calculate the distances to these objects. Surprisingly, these objects were discovered to be at distances which placed them well outside the Milky Way. They continued to be called ''nebulae'', and it was only gradually that the term ''galaxies'' replaced it.

=== Combining redshifts with distance measurements ===

[[File:Hubble constant.JPG|thumb|upright=1.45|Fit of [[#Redshift velocity|redshift velocities]] to Hubble's law.<ref name="Keel">{{cite book |last=Keel |first=W. C. |date=2007 |title=The Road to Galaxy Formation |url=https://books.google.com/books?id=BUgJGypUYF0C&pg=PA7 |pages=7–8 |edition=2nd |publisher=[[Springer (publisher)|Springer]] |isbn=978-3-540-72534-3 }}</ref> Various estimates for the [[#Determining the Hubble constant|Hubble constant]] exist.]]

The velocities and distances that appear in Hubble's law are not directly measured. The velocities are inferred from the redshift {{math|1=''z'' = ∆''λ''/''λ''}} of radiation and distance is inferred from brightness. Hubble sought to correlate brightness with parameter {{mvar|z}}.

Combining his measurements of galaxy distances with Vesto Slipher and [[Milton Humason]]'s measurements of the redshifts associated with the galaxies, Hubble discovered a rough proportionality between redshift of an object and its distance. Though there was considerable [[variance|scatter]] (now known to be caused by [[peculiar velocity|peculiar velocities]]—the 'Hubble flow' is used to refer to the region of space far enough out that the recession velocity is larger than local peculiar velocities), Hubble was able to plot a trend line from the 46 galaxies he studied and obtain a value for the Hubble constant of 500&nbsp;(km/s)/Mpc (much higher than the currently accepted value due to errors in his distance calibrations; see [[cosmic distance ladder]] for details).<ref name=damnh/>

==== Hubble diagram ====
Hubble's law can be easily depicted in a "Hubble diagram" in which the velocity (assumed approximately proportional to the redshift) of an object is plotted with respect to its distance from the observer.<ref>{{cite journal |last=Kirshner |first=R. P. |date=2003 |title=Hubble's diagram and cosmic expansion |journal=[[Proceedings of the National Academy of Sciences]] |volume=101 |issue=1 |pages=8–13 |bibcode=2004PNAS..101....8K |doi=10.1073/pnas.2536799100 |pmid=14695886 |pmc=314128 |doi-access=free }}</ref> A straight line of positive slope on this diagram is the visual depiction of Hubble's law.

=== Cosmological constant abandoned ===
{{main|Cosmological constant}}
After Hubble's discovery was published, [[Albert Einstein]] abandoned his work on the [[cosmological constant]], a [[Term (logic)|term]] he had inserted into his equations of general relativity to coerce them into producing the static solution he previously considered the correct state of the universe. The Einstein equations in their simplest form model either an expanding or contracting universe, so Einstein introduced the constant to counter expansion or contraction and lead to a static and flat universe.<ref name="mapcc">{{cite web |title=What is a Cosmological Constant? |url=http://map.gsfc.nasa.gov/universe/uni_accel.html |publisher=[[Goddard Space Flight Center]] |access-date=2013-10-17 }}</ref> After Hubble's discovery that the universe was, in fact, expanding, Einstein called his faulty assumption that the universe is static his "greatest mistake".<ref name=mapcc /> On its own, general relativity could predict the expansion of the universe, which (through [[Tests of general relativity|observations]] such as the [[Gravitational lens|bending of light by large masses]], or the [[Perihelion precession of Mercury|precession of the orbit of Mercury]]) could be experimentally observed and compared to his theoretical calculations using particular solutions of the equations he had originally formulated.

In 1931, Einstein went to Mount Wilson Observatory to thank Hubble for providing the observational basis for modern cosmology.<ref>{{cite book |last=Isaacson |first=W. |date=2007 |title=Einstein: His Life and Universe |url=https://archive.org/details/einsteinhislifeu0000isaa |url-access=registration |page=[https://archive.org/details/einsteinhislifeu0000isaa/page/n395 354] |publisher=[[Simon & Schuster]] |isbn=978-0-7432-6473-0 }}</ref>

The cosmological constant has regained attention in recent decades as a hypothetical explanation for [[dark energy]].<ref>{{cite web |date=28 November 2007 |title=Einstein's Biggest Blunder? Dark Energy May Be Consistent With Cosmological Constant |url=https://www.sciencedaily.com/releases/2007/11/071127142128.htm |website=[[Science Daily]] |access-date=2013-06-02 }}</ref>

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